Array processing in the presence of unknown nonuniform sensor noise: a maximum likelihood direction finding algorithm and Cramer-Rao bounds

We address the problem of estimating directions of arrival (DOAs) of multiple sources observed on the background of nonuniform white noise with an arbitrary unknown diagonal covariance matrix. A new deterministic maximum likelihood (ML) DOA estimator is derived. Its implementation is based on an iterative procedure which includes stepwise concentration of the log-likelihood (LL) function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge. New closed-form expressions for the deterministic and stochastic direction estimation Cramer-Rao bounds (CRBs) are derived for the considered nonuniform model. Our expressions can be viewed as an extension of the well-known results by Stoica and Nehorai (1989, 1990), and Weiss and Friedlander (1993, 1995) to a more general noise model than the commonly used uniform one. Simulation and experimental (seismic data processing) results illustrate the performance of the estimator and validate our theoretical analysis.